Differential Equation For the below ordinary differential equation with initial

Question

Differential Equation

For the below ordinary differential equation with initial conditions, state the order and dtermine if the equation is linear or nonlinear. Then find the solution of the ordinary differential equation, and apply the initial conditions. Verify your solution.

Differential Equation For the below ordinary differential equation with initial conditions, state the order and dtermine if the equation is linear or nonlinear. Then find the solution of the ordinary differential equation, and apply the initial conditions. Verify your solution. frac{dy}{dx} - frac{y}{x} = xe^{x}, y(1) = e-1

Explanation / Answer

dy/dx - y/x = xe^x

the function with y is -1/x

Multiplicating factor = e^(?-dx/x) = e^ -ln|x| = e^ ln|1/x| = 1/x
So, the equation becomes:
1/xdy/dx - y/x^2 = xe^x (1/x)
1/xdy/dx - y/x^2 = e^x
d/dx (y/x) = e^x
d (y/x) = e^x dx
y/x = e^x + C [Integrating]

y = xe^x + Cx

y(1)=e-1

e-1=e+c

c=-1

So, final solution is y = xe^x -x

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.